One form of evidence is the ionization energies of silicon. Nth ionization energy is the energy needed to remove the nth electron. There is a big jump going from the 4th ionization energy (~4000 kJ/mol) to the 5th ionization energy (~16000 kJ/mol).
Another form of evidence is the compounds silicon makes. Silicon forms $SiH_4$$\mathrm{SiH}_4$, $SiF_4$$\mathrm{SiF}_4$, $SiCl_4$$\mathrm{SiCl}_4$ and other compounds that imply 4 valence shell electrons.